Surd Calculations?

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. Surds are the root of numbers and not whole numbers.

Multiplication

square root of ab = square root of a x square root of b

square root of a x square root of a = a

Example: 

√2 × √6 = √12 (= 2× 6)

= √4 × √3

= 2√3

Addition and Subtraction

4√3 - 2√3 = 2√3

5√5 + 8√5 = 13√5

Note: 5√7 + 3√3 cannot be manipulated because the surds are different (one is √7 and one is √3)

Example:

Simplify √12 + √27

12 = 3 × 4. So √12 = √(3 × 4) = √3 × √4 = 2 × √3.

Similarly, √27 = 3√3.

Hence √12 + √27 = 2√3 + 3√3 = 5√3

 

 

 

Answered by Nita B. Maths tutor

10609 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Write down the value of 36^ 1/ 2


If two linear equations, y = x + 4 and y = 2x + c, intersect at x = 1, find c.


Quadratic Equations and factorising


Karen got 32 out of 80 on a Maths test. She got 38% on an English test. Which test did she do better in?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences